[EX09-141] The dry weight of a cork is another quality that does not affect the ability of the cork to seal the bottle, but it is a variable that is monitored regularly. The weights of the no. 9 natural corks (24 mm in diameter by 45 mm in length) have a normal distribution. Ten randomly selected corks were weighed to the nearest hundredth of a gram.

Dry Weight (in grams) 3.26 3.58 3.07 3.09 3.16 3.02 3.64 3.61 3.02 2.79

a. Does the preceding sample show sufficient reason to show the standard deviation of the dry weights is different from 0.3275 gram at the 0.02 level of significance?

A different random sample of 20 is taken from the same batch.

Dry Weight (in grams) 3.53 3.77 3.49 3.24 3.00 3.41 3.33 3.51 3.02 3.46 2.80 3.58 3.05 3.51 3.61 2.90 3.69 3.62 3.26 3.58

b. Does the preceding sample show sufficient reason to show the standard deviation of the dry weights is different from 0.3275 gram at the 0.02 level of significance?

c. What effect did the two different sample standard deviations have on the calculated test statistic in parts a and b? What effect did they have on the p-value or critical value? Explain.

d. What effect did the two different sample sizes have on the calculated test statistic in parts a and b? What effect did they have on the pvalue or critical value? Explain.